Integrated Gradients

Integrated Gradients is one of the few attribution methods that mathematically guarantees completeness: the sum of all pixel attributions equals the model's output difference from a baseline. For a diagnostic classifier, this means if a model outputs a 0.92 probability for 'malignant' and 0.08 for a blank baseline, the attributions across all voxels sum to exactly 0.84.

• Why it matters: No attribution mass is created or destroyed during the explanation process
• Contrast with Grad-CAM: Grad-CAM produces coarse localization maps but does not satisfy completeness
• Regulatory relevance: Auditors can verify that the total attributed evidence matches the prediction confidence

The method computes attributions by integrating the gradients of the model's output with respect to the input along a straight-line path from a baseline to the actual input. This path integral accumulates the contribution of each pixel as it transitions from absence to presence.

• Mathematical form: Attribution_i = (x_i - x'_i) × ∫₀¹ ∂F(x' + α(x - x'))/∂x_i dα
• Baseline selection: In medical imaging, a black image, blurred scan, or zero-signal reference serves as the 'absence of information' starting point
• Implementation: The integral is approximated using Riemann summation with 20-300 discrete steps along the path

Integrated Gradients satisfies two critical axioms that many saliency methods violate. Sensitivity ensures that if a single feature change alters the prediction, that feature receives non-zero attribution. Implementation invariance guarantees that functionally equivalent networks produce identical attributions regardless of architecture.

• Sensitivity example: If changing a single pixel from baseline to input value flips a diagnosis from 'benign' to 'malignant', that pixel must receive attribution
• Implementation invariance: Two networks with identical input-output behavior yield the same Integrated Gradients explanation, even if one uses ReLU and another uses GELU activations
• Contrast with LIME: LIME is model-agnostic but not implementation-invariant; different runs can produce different explanations

The choice of baseline critically shapes the explanation. In radiology, common baselines include a black image (zero pixel intensity), a Gaussian-blurred version of the input, or a population-average template from healthy patients. Each encodes a different definition of 'feature absence.'

• Black baseline: Attributes highlight any non-zero pixel that influences the prediction; may produce noisy saliency maps in dark regions of CT scans
• Blurred baseline: Removes high-frequency detail while preserving anatomical structure; attributions highlight diagnostically relevant edges and textures
• Clinical best practice: Use multiple baselines and aggregate attributions to avoid baseline-dependent artifacts in regulatory submissions

Integrated Gradients is increasingly referenced in FDA pre-submission meetings and SaMD audit trails as a method for demonstrating that a diagnostic model's decisions are based on clinically relevant anatomy rather than confounding artifacts. The completeness property enables quantitative verification.

• Audit trail integration: Store attributions alongside predictions for post-hoc review of every clinical decision
• Artifact detection: If a model attributes high importance to scanner bed markings or text annotations, Integrated Gradients will reveal this shortcut learning
• Clinician-in-the-loop: Radiologists can review overlaid saliency maps to calibrate their trust in AI-assisted diagnoses, reducing both automation bias and algorithm aversion